(1) Field of the Invention
The invention relates generally to the field of systems and methods for performing digital signal processing operations in connection with real-world signals, and more particularly to systems and methods for characterizing signals to determine their stochastic properties, that is, to determine weather they are random. If the signals are random, they may be determined to constitute noise, in which case, additional signal processing efforts which might be undertaken to process the signals can be avoided.
In a number of applications, it is desirable to be able to determine the likelihood that a signal is random. For example, an acoustic signal, received in an ocean environment, may constitute noise alone, or it may include some useful “information” along with a background noise. If the signal constitutes noise alone, its amplitude will be random, but if it includes information, it will not be random and further processing may be useful to identify the information. In some signal processing systems, it is assumed that the signal includes information, and the signal is processed to try to extract this information. It may be the case that the noise level of a received signal is so great that the information cannot be extracted, but if the signal is pure noise, effort will be wasted in any event. It is accordingly desirable to be able to determine the likelihood that a signal constitutes only noise, or if it also includes information, so that a determination can be made as to whether processing of the signal to extract the information would be useful.
(2) Description of the Prior Art
U.S. Pat. No. 5,966,414 to Francis J. O'Brien, incorporated by reference herein, discloses a signal processing system that processes a digital signal generated in response to an analog signal, and which includes a noise component and possibly an information component. An information processing sub-system receives the digital signal and processes it to extract any information component. A noise likelihood determination sub-system receives the digital signal and generates a random noise assessment that the digital signal comprises solely random noise, and controls the operation of the information processing sub-system in response to the random noise assessment.
In U.S. Pat. No. 6,397,234 to Francis J. O'Brien, et al, incorporated by reference herein, there is described an improved apparatus for characterizing a spatial arrangement among data points of a time series distribution in a data processing system wherein a classification or the time series distribution is required. The apparatus includes a display/operating system adapted to accommodate a pre-selected number N of data points generated during a pre-selected time interval. A first comparator is used for determining the data points in the input time series distribution having the largest and the smallest values, and determining the difference ΔY between the largest and smallest values of the data points. The apparatus further includes a virtual window creating device for creating a virtual window having an area equal to N*ΔY containing the input time series distribution of data points, and sub-dividing substantially the entirety of the virtual window into a plurality k of cells, each cell having the same polygonal geometric shape and defining an equal area. A counter is used for determining the number m of the cells containing at least one of the input data points of the input time series distribution, and another calculator determines the expected number of cells which would be occupied by at least one of the data points in the event that the input time series distribution was random according to the relation k*(1−e−N/k). A divider is provided for dividing m by k*(1−e−N/k). A second comparator device compares the output of the divider with unity. The input time series distribution is characterized as random when the output of the divider is closest to 1, clustered when the output of the divider is less than the output closest to 1, and uniform when the output of the divider is greater than the output closest to 1. A marking device associates the output of the second comparator with the input time series distribution, and an output device for transferring the marked input time series distribution to the data processing system for further processing.
The signal processing system comprises a transducer means for receiving an analog signal. The analog signal includes a noise component and possibly also an information component. A digital signal is generated from the analog signal. A noise likelihood determination sub-system receives the digital signal and generates a random noise assessment. The noise likelihood determination sub-system includes randomness statistic generating means for generating a randomness statistic in response to an interpoint spacing parameter statistic. An information processing sub-system receives the digital signal and extracts the information component if the random noise assessment indicates that the digital signal does not comprise solely random noise. The noise likelihood determination sub-system generates the random noise assessment in response to the randomness statistic.
The signal processing method includes the steps of receiving an analog signal, including a noise component, and possibly also an information component, and generating in response a digital signal which is represented by a plurality of sample points distributed over a selected region. The signal processing method further indicates a noise likelihood determination step of generating, in response to the digital signal, a random noise assessment that the digital signal comprises solely random noise. The noise likelihood determination step includes the step of generating the random noise assessment in response to a nearest-neighbor distance deviation assessment generated in response to distances between nearest-neighbor sample points in comparison with distances between a like number of nearest-neighbor reference points that are randomly distributed. Thereafter, an information processing step of receiving and processing the digital signal is undertaken to extract the information component, if it has been determined during the noise likelihood determination step that the random noise assessment indicates that the digital signal does not comprise solely random noise.
The signal processing method includes characterizing a spatial arrangement among a pre-selected number N of data points of a time series distribution of pre-selected duration in a display/operating system wherein a classification of the spatial arrangement of the time series distribution is required. The method comprises the steps of (i) inputting the time series distribution of no more than N data points, and no longer than the pre-selected time interval, into the display/operating system, (ii) determining the difference in value ΔY between a data point in the time series distribution having the greatest value and a data point in the time series distribution having the smallest value (iii) creating a virtual window having an area containing the time series distribution of data points, the area being equal to N*ΔY, (iv) subdividing substantially the entirety of the area of the window into a plurality k of cells, each cell having the same polygonal shape and defining the same area value, (v) determining a number m of the cells containing at least one of the data points of the time series distribution, (vi) determining an expected number M of cells containing at least one of the data points in the time series distribution in the event that the time series distribution is random in structure, and (vii) characterizing the input time series distribution as clustered in the event that m is less than M, random when m is equal to M, and uniform when m is greater then M.
A further consideration in accurate processing of signals relates to a condition known to statisticians as “edge-effect bias”, which can introduce significant errors into calculations, leading to an incorrect conclusion regarding the presence of noise in a distribution.
Edge effects arise because the distribution of distances assumes an unbounded area, but the observed nearest-neighbor (nn) distances are calculated from points in a defined study area. FIG. 1 illustrates such a point 2 near the outer edge 3, or border, of a study area 1, it is possible that the true nearest-neighbor is a point 4, just outside the study information component. An information processing sub-system receives the digital signal and processes it to extract the information component. A noise likelihood determination sub-system receives the digital signal and generates a random noise assessment that the digital signal comprises solely random noise, and controls the operation of the information processing sub-system in response to the random noise assessment.
Edge effects may be minimized by including a buffer area that surrounds the primary study area, with distances only calculated for points in the primary study area, but locations in the buffer area being available as potential nearest-neighbors. With a sufficiently large buffer area, this approach can eliminate edge effects, but it is wasteful since an appropriately large buffer area may contain many locations. A second approach is to apply an edge correction to the indicator function for those points that fall near the edges of the study area.